2log3+log300-log9
that would be log(3^2 * 300 / 9) = log(2700/9) = log300
In base 10 logs, that would be 2+log3
or, since 2log3 = log(3^2) = log9, you have
log9 + log300 - log9 = log300
To solve the expression 2log3 + log300 - log9, we need to recall some properties of logarithms.
1. The product property: log(a) + log(b) = log(ab)
2. The quotient property: log(a) - log(b) = log(a/b)
3. The exponent property: log(a^b) = b*log(a)
Applying these properties, we can simplify the expression step-by-step:
1. 2log3 + log300 - log9
2. Applying the exponent property, we rewrite log300 as log(100 * 3) = log(100) + log(3)
= 2 + log(3)
3. Now, we can rewrite the entire expression with the simplified log300: 2log3 + (2 + log3) - log9
4. Combining the like terms, we get: 2log3 + log3 + 2 - log9
5. Using the product property, we combine the log3 terms: 3log3 + 2 - log9
6. Lastly, we simplify the expression by rewriting log9 as log(3^2) = 2log3: 3log3 + 2 - 2log3
7. Combining the like terms, we obtain: log3 + 2
Therefore, the simplified form of the expression 2log3 + log300 - log9 is log3 + 2.